Alphabeta MathSmall-Cancellation Disc Diagrams and the Torsion Toolkit: Examples
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Pipeline-generated
How statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
1 · Prerequisites
- Binary Operations, Monoids, Groups and Subgroups
- Construction of the Natural Numbers
- Construction of the Real Numbers via Cauchy Sequences
- Construction of the Real Numbers via Dedekind Cuts
- Cosets, Index and Lagrange's Theorem
- Countability and Uncountability
- Finite Counting, Factorials and Binomial Coefficients
- Free Groups and Presentations
- Normal Subgroups and Quotient Groups
- Relations, Functions, and Quotients
- Small-Cancellation Disc Diagrams and the Torsion Toolkit
- The ZFC Axioms and the Basic Set Constructions
2 · Logical flowchart
3 · Items
Example
Curvature ledger for a two cell diagram
Example
A three shell after arc reduction
Example
Relator root versus proper power
Counterexample